Simplify the following expression: $k = \dfrac{3z^2 + z}{5xz + 5yz} + \dfrac{5z^2 - 5z}{5xz + 5yz}$ You can assume $x,y,z \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{3z^2 + z + 5z^2 - 5z}{5xz + 5yz}$ $k = \dfrac{8z^2 - 4z}{5xz + 5yz}$ The numerator and denominator have a common factor of $z$, so we can simplify $k = \dfrac{8z - 4}{5x + 5y}$